A device of this general type is known from European patent document B10,258,637. In that device, dosing is implemented by manually pushing a button so that a cartridge of liquid containing the medicine is somewhat compressed and, as a result, a given quantity of medicine is fed in the form of droplets to an atomizer. In such manual dosage the compression applied to the cartridge can vary within wide limits and, accordingly, the dispensed quantity of medicine cannot be predetermined. When the discharge rate of the medicine liquid is excessive, then in spite of the desired droplet form, there will be a continuous liquid jet and as a result the liquid medicine no longer can be deposited on the atomizer dish. Another drawback of this known inhaling device is that dosage is restricted to a single droplet, that is to about 20 .mu.ltr (microliters).